Mathjax

General

TitleFormulaMarkdown
Variables, $x_1$, $z_{3,4}$
Square, $a^2$, $$x^y$, $2^{n-1}$
Square Root, $\sqrt{9}$, $\sqrt{x}$
Logarithm, $\log{}x$, $\log_{2}x$
Limits$\lim_{x\to \infty}$
Fraction, $\frac{1}{2}$, $\left(-\frac{1}{2}\right)^n$
Infinity$infty$
Real numbers, Integers, Natural numbers, Rational numbers, Irrational numbers, , , , $\Bbb R$, $\Bbb Z$, $\Bbb N$, $\Bbb Q$, $\Bbb P$
Absolute Value, , , $\vert{x}\vert$, $\vert\frac{x}{2}\vert$, $\lfloor{x}\rfloor$, $\lceil{x}\rceil$
Arithmetic, , , $4 + 3$, $3 - 3$, $3\times 3$, $3\div 3$
Factorial$n!$
Trigonometric functions, , $\sin\theta$, $\cos\theta$, $\tan\theta$
Greater or Less, , , $a\gt b$, $a\geq b$, $a\lt b$, $a\leq b$
Much Less Than, Much Greater Than, $a \ll b$, $b \gg a$
Equation, , $a=b$, $a\neq b$, $a\approx b$
Times Dot$a\cdot b=ab$
Divide Fraction$a/b=\frac{a}{b}$
Trinomial Equation$a^2 + b^2 = c^2$
Matrix Parentheses$$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
Matrix Brackets$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
Matrix Equation$$\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc$$
Set, , $x\in A$, $A\ni x$, $x\notin A$
Subset, , $A\subset B$, $A\subseteq B$, $A \not \subset B$
Intersection & Union, , $A\cap B$, $A\cup B$, $\overline{A}$
Logical Operators$$ \forall X, \wedge X, \vee X, \neg X, \exists A A \implies B $$
Quadratic Formula$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
Binomial$\sqrt{3x-1}+(1+x)^2$
Differentiation, , $f'$, $f^{(n)}$, $D_x f$
Integral$\int_0^1 f(x) dx$
Sigma$\displaystyle \sum_{i=1}^k$
Integral Large$\displaystyle \int_{-\infty }^{\infty}f(x)dx$
Max Sample$$\max(a,b)=\begin{cases}a&(a\geqq b)\\b&(a\lt b)\end{cases}$$
Piecewise Equations$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$
Tables$$\begin{array}{clcr} n & \text{Left} & \text{Center} & \text{Right} \ \hline 1 & 0.24 & 1 & 125 \ 2 & -1 & 189 & -8 \ 3 & -20 & 2000 & 1+10i \end{array}$$
Set Comprehensions\{x \text{ if x is even} \mid x^2\in\Bbb Z\}$\{x \text{ if $x$ is even} \mid x^2\in\Bbb Z\}$
NameRunning TimeMarkdown
Big O [micron] or $\mathcal{0}$ or $O$
Big Omega$\Omega$
Big Theta$\Theta$
Small O [micron]$o$
Small Omega$\omega$
On the order of$\sim$

Common Time and Space Complexity

NameRunning TimeMarkdown
Constant Time$O(1)$
Logarithmic Time$O(\log{}n)$
Linear Time$O(n)$
Quasilinear Time$O(n\log{}n)$
Quadratic Time$O(n^2)$
Cubic Time$O(n^3)$
Factorial Time$O(n!)$
Exponential Time$O(2^n)$